1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "delayed_updating/reduction/dbfr.ma".
16 include "delayed_updating/reduction/ibfr_unwind.ma".
18 include "delayed_updating/unwind/unwind2_prototerm_constructors.ma".
20 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
22 (* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
24 (* Main destructions with ibfr **********************************************)
26 theorem dbfr_des_ibfr_push (f) (t1) (t2) (r): t1 ϵ 𝐓 →
27 t1 ➡𝐝𝐛𝐟[r] t2 → ▼[⫯f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[⫯f]t2.
29 * #p #b #q #m #n #Hr #Hp #Hb #Hm #Hn #Ht1 #Ht2 destruct
30 @(ex7_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
31 [ -H0t1 -Hp -Hb -Hm -Hn -Ht1 -Ht2 //
32 | -H0t1 -Hb -Hm -Hn -Ht1 -Ht2 /2 width=1 by path_guard_structure/
33 | -H0t1 -Hp -Hm -Hn -Ht1 -Ht2 //
34 | -H0t1 -Hp -Hb -Hn -Ht1 -Ht2
35 /2 width=2 by path_closed_structure_depth/
36 | -H0t1 -Hp -Hb -Hm -Ht1 -Ht2
37 /2 width=2 by path_closed_structure_depth/
38 | lapply (in_comp_unwind2_path_term (⫯f) … Ht1) -H0t1 -Hp -Hb -Hm -Ht2 -Ht1
39 <unwind2_path_d_dx <tr_pap_succ_nap >list_append_rcons_dx >list_append_assoc
40 <nap_unwind2_rmap_append_closed_Lq_dx //
41 | lapply (unwind2_term_eq_repl_dx (⫯f) … Ht2) -Ht2 #Ht2
42 @(subset_eq_trans … Ht2) -t2
43 @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
44 [ @fsubst_eq_repl [ // | // ]
45 @(subset_eq_trans … (unwind2_term_iref …))
46 @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
47 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
48 @(subset_eq_trans … (lift_unwind2_term_after …))
49 @unwind2_term_eq_repl_sn
50 (* Note: crux of the proof begins *)
51 /2 width=1 by unwind2_rmap_uni_crux/
52 (* Note: crux of the proof ends *)
54 | /2 width=2 by ex_intro/
60 theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
61 t1 ➡𝐝𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
62 #f #t1 #t2 #r #Ht1 #Ht12
63 lapply (dbfr_des_ibfr_push (𝐢) … Ht1 Ht12) -Ht1 -Ht12 #Ht12
64 /2 width=1 by ibfr_structure_unwind_bi/